Curious,what made you reach the conclusion of him being the 3rd or 4th generation?
Considering it's perfectly normal to have kids during your twenties and you get 9+ generations easily.
Even assuming they delayed that like crazy and got kids around the fourties every generation it's still atleast 5-6generations.
(Can't really delay it much beyond that for biological reasons.)
3-4 lifespans between those events and the new prince sounds more likely, is that perhaps what you meant/thought of?